Asymptotic Notation Calculator

---
name: asymptotic-notation-calculator
description: Automated derivation and simplification of Big-O, Big-Omega, and Big-Theta expressions for algorithm analysis
allowed-tools:
  - Bash
  - Read
  - Write
  - Edit
  - Glob
  - Grep
metadata:
  specialization: computer-science
  domain: science
  category: algorithm-analysis
  phase: 6
graph:
  domains: [domain:computer-science]
  specializations: [specialization:theoretical-computer-science]
  skillAreas: [skill-area:np-hard-heuristics, skill-area:mathematical-reasoning, skill-area:dynamic-programming]
  workflows: [workflow:research-grant-lifecycle]
  roles: [role:computational-scientist, role:research-engineer]
---

# Asymptotic Notation Calculator

## Purpose

Provides expert guidance on analyzing, simplifying, and comparing asymptotic complexity expressions for algorithm analysis.

## Capabilities

- Parse and simplify asymptotic expressions
- Compare complexity classes
- Identify dominant terms
- Handle logarithmic, polynomial, and exponential factors
- Generate LaTeX-formatted notation
- Prove asymptotic relationships

## Usage Guidelines

1. **Expression Analysis**: Parse complexity expressions into canonical forms
2. **Simplification**: Apply dominance rules to simplify nested expressions
3. **Comparison**: Determine ordering between complexity classes
4. **Documentation**: Generate properly formatted asymptotic notation
5. **Verification**: Prove Big-O, Big-Omega, and Big-Theta relationships

## Tools/Libraries

- SymPy
- Symbolic computation
- LaTeX rendering